`a_0 = 3, a_1 = 3, a_4 = 15` Find a quadratic model for the sequence with the indicated terms.

You need to remember what a quadratic model is, such that:

`a_n = f(n) = a*n^2 + b*n + c`

The problem provides the following information, such that:

`a_0 = 3 => f(0) = a*0^2 + b*0 + c =>  c = 3`

`a_1 = 3 => f(1) = a*1^2 + b*1 + c => a + b + c = 3`

`a_4 = 15 => f(4) = a*4^2 + b*4 + c => 16a + 4b + c = 15`

You need to replace 3 for c in equation `a + b + c = 3` :

`a + b + 3 = 3 => a + b = 0`

You need to replace 3 for c in equation `16a + 4b + c = 15` :

`16a + 4b + 3 = 15 => 16a + 4b = 12 => 4a + b = 3`

Subtract `a + b = 0` from `4a + b = 3` , such that:

`4a + b - a - b = 3`

`3a = 3=> a = 1`

Replace 1 for a in equation `a + b = 0`  such that:

`1 + b = 0 => b = -1`

Hence, the quadratic model for the given sequence is `a_n = n^2 - n + 3.`